84 citations · 521 across the 32 of their papers we have counts for
10 papers · 1 filter
Twenty Vertex model and domino tilings of the Aztec triangle
Philippe Di Francesco
We show that the number of configurations of the 20 Vertex model on certain domains with domain wall type boundary conditions is equal to the number of domino tilings of Aztec-like…
Twenty-Vertex model with domain wall boundaries and domino tilings
Philippe Di Francesco, Emmanuel Guitter
We consider the triangular lattice ice model (20-Vertex model) with four types of domain-wall type boundary conditions. In types 1 and 2, the configurations are shown to be equinum…
Truncated determinants and the refined enumeration of Alternating Sign Matrices and Descending Plane Partitions
Philippe Di Francesco
Lecture notes for the proceedings of the workshop "Algebraic Combinatorics related to Young diagram and statistical physics", Aug. 6-10 2012, I.I.A.S., Nara, Japan.
An inhomogeneous Lambda-determinant
P. Di Francesco
We introduce a multi-parameter generalization of the Lambda-determinant of Robbins and Rumsey, based on the cluster algebra with coefficients attached to a T-system recurrence. We…
T-systems with boundaries from network solutions
Philippe Di Francesco, Rinat Kedem
In this paper, we use the network solution of the -system to derive that of the unrestricted -system, equivalent to the octahedron relation. We then present…
Positivity of the T-system cluster algebra
P. Di Francesco, R. Kedem
We give the path model solution for the cluster algebra variables of the -system with generic boundary conditions. The solutions are partition functions of (strongly) non-…
Geodesic Distance in Planar Graphs: An Integrable Approach
P. Di Francesco
We discuss the enumeration of planar graphs using bijections with suitably decorated trees, which allow for keeping track of the geodesic distances between faces of the graph. The…
Combinatorics of bicubic maps with hard particles
J. Bouttier, P. Di Francesco, E. Guitter
We present a purely combinatorial solution of the problem of enumerating planar bicubic maps with hard particles. This is done by use of a bijection with a particular class of blos…
Planar maps as labeled mobiles
J. Bouttier, P. Di Francesco, E. Guitter
We extend Schaeffer's bijection between rooted quadrangulations and well-labeled trees to the general case of Eulerian planar maps with prescribed face valences, to obtain a biject…
A Bijection between classes of Fully Packed Loops and Plane Partitions
P. Di Francesco, P. Zinn-Justin, J. -B. Zuber
It has recently been observed empirically that the number of FPL configurations with 3 sets of a, b and c nested arches equals the number of plane partitions in a box of size a x b…